Analytical network processes（サービスサイエンスの事はじめ 高木英明先生 筑波大学出版会）

#ANP

library(dplyr)

D1=t(matrix(c(1,5,1/5,1),ncol=2,nrow=2))

D2=t(matrix(c(1,1/3,3,1),ncol=2,nrow=2))

D3=t(matrix(c(1,1/7,7,1),ncol=2,nrow=2))

v1=eigen_vector_D1=sqrt(apply(D1,1,prod))/sum(sqrt(apply(D1,1,prod)))

v2=eigen_vector_D2=sqrt(apply(D2,1,prod))/sum(sqrt(apply(D2,1,prod)))

v3=eigen_vector_D3=sqrt(apply(D3,1,prod))/sum(sqrt(apply(D3,1,prod)))

D_bar=t(matrix(c(1,9,3,1/9,1,1/5,1/3,5,1),nrow=3,ncol=3))

w1=(apply(D_bar,1,prod)^(1/ncol(D_bar)))/sum(apply(D_bar,1,prod)^(1/ncol(D_bar)))

mat1=matrix(c(1,1,1,1,1,1,1,1,1),nrow=3,ncol=3) 

mat2=t(matrix(c(1,1/3,1,3,1,3,1,1/3,1),nrow=3,ncol=3)) 

mat=(mat1^(16/22))*(mat2^(6/22))

w2=(apply(mat,1,prod)^(1/ncol(mat)))/sum(apply(mat,1,prod)^(1/ncol(mat)))

w=cbind(w1,w2);v=cbind(v1,v2,v3)

wv=w%*%v

wv_eigen_values=eigen(wv)$values

wv_eigen_vectors=eigen(wv)$vectors

q=wv_eigen_vectors[,1]/sum(wv_eigen_vectors[,1])

p=v%*%q



#super_matrix(5.12)

super_matrix=array(0,dim=c(5,5))

super_matrix[3:5,1:2]=w

super_matrix[1:2,3:5]=v

#(5.8)

A=matrix(rep(0,6*6),ncol=6,nrow=6)

A[1,1]=1
A[2:3,1]=v1
A[4:6,2:3]=w

#Frobenius theorem

max_eigen=max(eigen(A)$values)

p=rep(0,nrow(A))

p[1]=A[1,1]

for(i in 2:nrow(A)){

p[i]=sum(A[i,1:(i-1)]*p[1:(i-1)])/(max_eigen-A[i,i])  

}


eigen_vector=eigen(super_matrix)$vectors[,1]

p=eigen_vector[1:2]/sum(eigen_vector[1:2])

q=eigen_vector[3:5]/sum(eigen_vector[3:5])